Much like history has recently found enough collaborating evidence to suggest [physical] unicorn legends -- especially the very old use of the term -- were referring to the white rhino, mermaids have long been known to likely be other now-known sea creatures, largely marine mammals. In fact, there is a journal entry by an early European explorer of North America about 'mermaids,' which is well-known to reference his first encounter with manatees.
It has long been the habit of humans to anthropomorphize animals, and the misunderstanding of things not seen up-close, or recalled from memory long after a far-off glance, has led to a lot of misconceptions which eventually became mythical creatures. Of course, we as a species also have a phenomenal imagination.
So physically, they do not exist.
Non-physically, who's to say? It's a matter of belief, and not fact. Some people may say they have encountered them as spirits or astral entities, while others may still insist otherwise.